High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems - Lee, Khai Chien; Senu, Norazak; Ahmadian, Ali; Ibrahim, Siti Nur Iqmal (Springer Medizin, 2021)
Three stage sixth-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods are proposed for solving u'''(t) = f(t, u(t), u'(t)). The idea of construction is based on linear composition of the set functions ewt and e-wt for exponentially fitted and eiwt and e-iwt for trigonometrically fitted with weR to integrate initial value problems. The selected coefficients of two-derivative Runge–Kutta-type method are modified to depend on the principle frequency of the numerical problems to construct exponentially fitted and trigonometrically fitted Runge–Kutta-type direct methods, denoted as EFTDRKT6 and TFTDRKT6 methods. The numerical experiments illustrate competence of the new exponentially fitted and trigonometrically fitted method compared to existing methods for solving special type third-order ordinary differential equations with initial value problems.